Is there a relationship between the dollars spent each week on recreation and the number of members of the family? Do larger families spend more on recreation? Ten Chicago families shared the following information:
Family Size 3 6 5 6 6 3 4 4 5 3
Amount Spent 99 104 151 129 142 111 74 91 119 91
a. What is the dependent variable (Y) in this situation?
b. What is the independent variable (X) in this situation?
c. Calculate ∑X, ∑Y, ∑XY, ∑X2, and ∑Y2.
d. Calculate SSXX, SSYY, and SSXY.
e. Calculate the estimated slope coefficient, b1.
f. Calculate the estimated y-intercept, b0.
g. Interpret the estimated slope coefficient.
h. Predict the recreational spending for a family of size 5.
i. If there are families of that size in the data set, what are the residuals for those observations?
j. Test the explanatory power of the model at a 5% level of significance.
k. Test if there is a positive relationship between family size and recreational spending. Use alpha = 0.01.
l. What is the excel command used to produce the p-value associated with the test in part k?
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